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" IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... - Page 161
by John Keill - 1733 - 397 pages
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Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - Dick bequest for elevating the character and position of the parochial schools and schoolmasters in the counties of Aberdeen, Banff and Moray - 1865 - 401 pages
...ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar...
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 404 pages
...described about a circle are together equal to the other two opposite sides. 5. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and &c. 6....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...GFL, and BA is to AE as GFis to FL. [VI. Definition I. And, because the triangles ABE and FGL have one angle of the one equal to one angle of the other, and the side* about these equal angles proportionals, therefore the triangle ABE is equiangular to...
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The Edinburgh university calendar

Edinburgh univ - 1868
...the segments of the other. 4. To inscribe a circle in a given triangle. 5- Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 6. Find the continued product of (x + y + z), ( - x + y + z), (x - y +),...
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(Report).

Elizabethan club - 1880
...the line which meets it, the line which meets shall touch the circle. 49 10. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular to each other,...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...the hexagon, prove that the square on AC is three times the square on AB. 10. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles are similar. If two chords AB, AC...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...the triangle DEF. Wherefore, if two triangles &c. QED PROPOSITION 7. THEOREM. If two triangles have one. angle of the one equal to one angle of the other, and the sides about two other angles proportionals; then, if each of the remaining angles be either...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 399 pages
...Angle A — angle FMN = angle D; ) ,„. Angle B = angle FMN = angle E. \ ^ ' QED THEOREM VII. 393. Two triangles having one angle of the one equal to one angle of the other, and the sides containing these angles proportional, are similar. Hypothesis. ABC and A'B'C', two triangles...
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The Cambridge Examiner, Volume 4

Education, Higher - 1884
...homologous sides shall either be equal, or be together equal to two right angles. 15. Triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Algebra. Junior, Senior,...
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